Is this what you are looking for?

sage: P.<x> = GF(2)[]
sage: f = P.random_element(degree=31)
sage: f.is_irreducible()             
False
sage: while f.degree() != 31 or f.is_irreducible() is False:
....:     f = P.random_element(degree=31)
....:     
sage: f.is_irreducible()
True
sage: f.degree()
31


On Wednesday 21 Mar 2012, clinton bowen wrote:
> Hello,
> 
> Is there a way to derive irreducible polynomials of degree n for the field
> F 2? I am looking for the set of all irreducible polynomials of degree
> n=31. If so, how is it done in sage?
> 
> Thanks,
> 
> clinton

Cheers,
Martin

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